How to find the number of solutions to an equation

Asked by admin @ 09/11/2021 in Mathematics viewed by 300 People

Find the number of real number solutions for the equation. x2 + 5x + 7 = 0

0
2
1
cannot be determined

Answered by admin @ 09/11/2021

Steps:

Discriminant Formula: D = b² - 4ac (With a = x² coefficient, b = x coefficient, and c = constant)

So to find the number of solutions this quadratic equation has without actually solving the equation, we are going to be using the discriminant formula. Plug in the numbers and solve:

$D=5^2-4*1*7\\D=25-28\\D=-3$

Now, here are the rules with discriminants:

D > 0; there are 2 real solutions in the equation
D = 0; there is 1 real solution in the equation
D < 0; there are no real solutions in the equation

Answer:

Since -3 is less than 0, this means that there are 0 real solutions in this equation.

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